CHARACTERIZATION OF THE Hedera helix L. LEAVES GEOMETRY BASED ON SOME DIMENSIONAL PARAMETERS AND CALCULATED RATIOS

. The study analyzed leaves of ivy, Hedera helix L., in order to characterize the geometry of the leaves. The leaf samples were taken from the Protected Area "Padurea Cenad", Timis County, Romania. The dimensions of the leaves (L, w) were determined by measurement, with a precision of 0.5 mm. The leaves were scanned, 1:1 ratio. From the analysis of the leaf images, the perimeter (Per) and scanned leaf area (SLA) were determined. The correction factor (CF), specific to ivy leaves, was found (CF=0.69) for the purpose of use in non-destructive methods of measuring the leaf area (MLA) based on a general formula of the type MLA=L·w·CF. The fitting relationship between MLA and SLA was described by a linear equation, under statistical safety conditions (p<0.001). Different ratios between leaf parameters were calculated in order to characterize the leaf geometry (L/w, Per/L, Per/w, SLA/L, SLA/w, SLA/Per, MLA/L, MLA/w). Different levels of correlation between basic leaf parameters, leaf surface and the calculated ratios were identified, with statistical certainty for most cases (p<0.001). Both from the correlation analysis and from the regression analysis, a tighter relationship of MLA with foliar parameters (L, w) was found than in the case of SLA (based on r, R 2 , F test, and RMSEP values). From the analysis of the values obtained for the coefficient of variation (CV), the highest variability was found in the case of SLA (CV SLA =38.6726), followed by MLA (CV MLA =36.8300), and the lowest variability in the case of the ratio Per/w (CV Per/w =10.1515). The regression analysis facilitated the finding of some equations that described the variation of SLA and MLA with leaf parameters (L, w, Per) in conditions of statistical safety (p<0.001). 3D graphic models and in the form of isoquants were also generated, which represented the MLA variation in relation to the dimensional parameters of the ivy leaves studied.


INTRODUCTION
Ivy, Hedera helix L. is a climbing plant, which is part of the Araliaceae Family. It is an evergreen plant, growing up to 20 -30 m. The growth can take place at ground level, as a cover, or in height, if there is a suitable support (vertical surfaces -trees, walls, rocks) on which it is fixed with the roots air (Metcalfe, 1975;Melzer et al., 2010Melzer et al., , 2012Bunk et al., 2019).
Ivy grows on soils with variable pH, but prefers a neutral reaction (ideal pH = 6.5). It prefers moist, shaded places and does not tolerate direct and intense sunlight, and the change in climatic conditions has an impact on the expansion of ivy in forest areas (Kucharski et al., 2019).
The leaves have an alternate position, varying in length between 5 -10 cm and there are two types, juvenile leaves (palmated, with five lobes, on creeping and climbing stems) and adult leaves (cordate, unlobed, on fertile flowering stems), flowers of the type umbel 3 -5 cm in diameter, purple-black fruits 6 -8 mm in diameter (Metcalfe, 2005).
Ivy has been studied in relation to different extracts of bioactive compounds, from leaves for pharmaceutical and medicinal purposes, for the treatment of some diseases (Rai, 2013;Bezruk et al., 2020;Sierocinski et al., 2021).
In relation to certain specific conditions for some areas, ivy has been studied as an invasive plant (Yang et al., 2013;Strelau et al., 2018).
Ivy grows in various open areas, in suitable vegetation conditions, but at the same time it is cultivated as an ornamental plant (Metcalfe, 1975;Chung et al., 2018). As an ornamental plant, the growth of ivy plants has been studied in relation to different substrates, regime of nutrients and water (Kresten et al., 2001).
Ivy was studied in relation to urban areas, and it was found to have an important bio-protective role, to absorb dust, fine powders and pollutants at leaf level, especially in areas with intense traffic (Sternberg et al., 2010). Various other species and quality indicators of urban ecosystems were used in relation to specific study objectives (Datcu et al., 2017).
The protective role of ivy plants (through extensive foliar covering of the walls) was studied in order to thermally protect (improvement of the thermal regime of bricks, with savings of up to 37%) certain buildings with stone walls, or other resistant materials for constructions (Cameron et al., 2015;Coombes et al., 2018).
From another perspective, the growth of ivy plants was evaluated in relation to its aggressiveness in relation to some monuments that it can affect (Bartoli et al., 2016). 8 The present study analyzed leaves of ivy (Hedera helix L.), in order to characterize the geometry of the leaves based on the leaf parameters, the leaf area and some ratios calculated between the elements of the leaf geometry considered.

MATERIAL AND METHODS
In relation to the objectives of the study, about 100 leaves (leaves on creeping and climbing stems) of ivy (Hedera helix L.) were taken at random from the area of the "Cenad Forest" Protected Area in order to analyze and characterize the geometry of the leaves.
From the set of leaf samples, 50 randomly representative leaves were analyzed by size group (example leaf in figure 1), for which the dimensions, length (L) and width (w), were measured. The measurements were made with a ruler, with a precision of about 0.5 mm. The leaves were scanned individually, at a scale of 1:1. From the analysis of the images (Rasband, 1997) the perimeter (Per) and scanned leaf area (SLA) were determined. In order to facilitate the determination of the measured leaf area (MLA) by non-destructive methods, based on the dimensions of the leaves (L, w), according to relation (1), the determination of the optimal value of the correction factor (CF) specific to ivy leaves was considered. For this, the model proposed by Sala et al. (2015) was used. (1) where: MLA -measured leaf area; L -leaf length; W -leaf width; CF -the specific correctin factor for ivy leaves.
In order to characterize the geometry of the leaves, a series of ratios between determined parameters and leaf indices were calculated (L/w, Per/L, SLA/L, SLA/w, MLA/L, MLA/w).
To certify the optimal value of the correction factor, the minimum error (ME) was calculated as the difference between MLA and SLA (considered as reference). The RMSEP statistical safety parameter, relation (2), was also calculated, in order to verify and certify the optimal value for the determined CF. (2) Descriptive statistical analysis was used for the general analysis of the obtained experimental data. Interdependence relationships between parameters and foliar indices considered by correlation analysis (Pearson) were quantified, for which statistical certainty was also determined (p < 0.05; p < 0.01, p < 0.001).
Linear regression analysis and multiple regression were used to describe the fit relationship between MLA and SLA, as well as other interdependence relationships between determined parameters and foliar indices, and for safety, p and R 2 parameters, and the F-test, were considered.
The variability within the data series was quantified for each parameter and foliar index, both by calculation (coefficient of variation, CV) and by the graphic method (Diversity profiles).
For the analysis and statistical processing of the experimental data, the mathematical calculation module from EXCEL, and the software PAST (Hammer et al., 2001), Wolfram Alpha (2020) and JASP (2022) were used.

RESULTS AND DISCUSSIONS
The values of the dimensional parameters leaf length and width (L, w), perimeter (Per), scanned and measured leaf surface (SLA, MLA), as well as various ratios calculated between the dimensional parameters of ivy leaves are presented, in the form of descriptive statistics, in table 1, with the graphic distribution in matrix plot format in figure 2.  Based on the model proposed by Sala et al. (2015) the value of the specific correction factor (CF) for ivy leaves was found. The average error (ME) was calculated as the difference between MLA and SLA at a series of 11 consecutive values of the correction factor (CF), including the optimal value, and the obtained results are presented in table 2.
The graphic representation of the ME, and the standard error (SE), in relation to the series of CF values considered in the analysis, is shown in figure 2. From the analysis of the obtained values and the graphic distribution, it was found that the optimal value for the determined correction factor was CF=0.69, at which the calculated value for the mean error (ME) was minimal, ME=0.02 cm 2 . The RMSEP statistical parameter additionally calculated for the 11 data sets from the series of CF values considered, confirmed that the value 0.69 for the correction factor represents the optimal value, at which the RMSEP value obtained was the minimum (RMSEP=8.1472), table 2.  The fitting relationship between MLA and SLA was evaluated by regression analysis and the linear equation  The level of variability in the data set, for the considered elements, was evaluated based on calculation (coefficient of variation, CV) and based on graphics analysis (Diversity profiles). From the analysis of the values obtained for the coefficient of variation, the highest variability was found in the case of SLA (CVSLA=38.6726), followed by MLA (CVMLA=36.8300), and the lowest variability in the case of the Per/w ratio (CVPer/w=10.1515 ).
The graphic analysis, of the diversity profile type, led to figure 4, and confirms the high variability in the case of SLA and MLA and a low variability in the case of the ratio Per/w, respectively Per/L. The correlation analysis highlighted interdependence relationships of different intensity levels and statistical safety conditions between the leaf elements considered. SLA was determined by analyzing the scanned images, and moderate correlations were recorded between SLA and leaf dimensional parameters with L (r=0.787, p<0.001), and strong correlations with w (r=0.899, p<0.001).
MLA was calculated based on the dimensional parameters of the leaves (L, w) and the correction factor (CF=0.69), relation (1). As a result, higher correlation levels were found between MLA and dimensional parameters, respectively strong correlation with L (r=0.884, p<0.001), and very strong correlation with w (r=0.901, p<0.001).
With leaf perimeter (Per), SLA and MLA showed very strong correlations (r=0.911, p<0.001 for SLA; r=0.955, p<0.001 for MLA). The values of the correlation coefficient and the statistical safety parameter (p) calculated for the elements considered in the description of the geometry of ivy leaves (dimensional parameters, leaf surface, different calculated ratios), are presented in table 3. The SLA values were described in relation to L, w and Per by equation (4), under statistical safety conditions (R2=0.961, p<0.001, F=390.131).
The variation of MLA in relation to leaf parameters L, w and Per was described by equation (5), under statistical safety conditions (R 2 =0.970, p<0.001, F=513.289). Both from the correlation analysis and from the regression analysis, a closer relationship of MLA with foliar parameters (L, w) was found than in the case of SLA (values r, R 2 , F test). This is as a result of the fact that the SLA determination was made through imaging analysis, which was based on the pixels occupied by the leaf surface of each leaf, while the MLA was determined based on the parameters L and w, as a direct relationship, adjusted by the correction factor (CF), relation (1). This was also confirmed by the RMSEP parameter, with values of RMSEP=13.9767 in the case of SLA, respectively RMSEP=12.1734 in the case of MLA.
The MLA variation was analyzed in relation to L and Per (R 2 =0.994, p<0.001), equation (6), respectively between w and Per (R 2 =0.991, p<0.001), equation (7), as a direct relationship and of interaction between the considered elements. The graphic distribution of MLA in relation to L (x-axis) and Per (y-axis) is shown in figure 5 (a) in the form of a 3D model, and in figure 5 (b) in the form of isoquants.
The graphic distribution of MLA in relation to w (x-axis) and Per (y-axis) is shown in figure 6 (a) in the form of a 3D model and in figure 6 (b) in the form of isoquants. From the analysis of the graphic distributions, it was found that in the variation of MLA in relation to L and Per, Per had a predominant contribution, and a more balanced contribution was in the case of w and Per parameters. (6) where: MLA -measured leaf area; x -leaf length -L; y -leaf perimeter -Per; a, b, c, d, e, f -coefficients of the equation (6) where: MLA -measured leaf area; x -leaf width -w; y -leaf perimeter -Per; a, b, c, d, e, f -coefficients of the equation (7)  Through the fractal analysis of the geometry of the leaves, it was possible to classify some apple varieties based on the obtained fractal dimension (D), which eloquently expressed the specificity of the geometry (topology) of the leaves .
For the study and characterization of leaves in different plant species, from leaves with common shapes to leaves with special shapes, different ratios, such as between width and length, perimeter and leaf surface, were taken into account, calculated and interpreted, but also others, and the obtained results facilitated the leaves description in terms of statistical safety (r > 0.9, p<0.001, low RMSE values) of the different types of leaves (Shi et al., 2019(Shi et al., , 2021. For the evaluation of the spatial morphology of the leaves, a case study of eggplant leaves, Wang et al. (2021) used a method based on three-dimensionality, which assumed the extraction of information about the shape, length and width of the leaves, and the results presented a high level of statistical certainty, assessed on the basis of the coefficient of determination (R 2 ).
As a proportional relationship between the length and width of the leaves, He et al. (2020) communicated a general formula for determining the leaf surface in six Magnoliaceae species. The authors recorded a high level of statistical certainty (r=0.84, p<0.05) regarding the relationship between the surface of the leaves and the ratio between leaf width and length (W/L).
In the context of interest in the analysis and evaluation of plant leaves based on leaf parameters, the present study evaluated ivy leaves and makes a significant contribution to the specialized literature, with values of leaf parameters, leaf surface, and some ratios calculated for the purpose of describing the geometry ivy leaves, Hedera helix L.

CONCLUSIONS
In relation to the proposed objective, the study facilitated the determination of the basic leaf parameters (L, w, Per), the leaf surface (SLA, MLA), and the calculated ratios (L/w, Per/L, SLA/L, SLA/w , MLA/L, MLA/w), for the description of the geometry of ivy leaves, Hedera helix L.
The correction factor (CF) specific to ivy leaves was determined on the basis of the studied leaf samples (CF=0.69), for the purpose of use in the measurement of leaf area (MLA) by non-destructive methods.
The variability of the elements considered (leaf parameters, leaf surface, calculated ratios) for the description of the geometry of ivy leaves were evaluated, and the elements with high or low variability in the description of the geometry of the leaves were found.
Equation-type models were obtained, under statistical safety conditions (p<0.001) that described the variation of SLA and MLA in relation to L, w or Per, and 3D graphic models or in the form of isoquants were obtained that graphically reproduced the leaf surface variation in the studied ivy leaf samples.